1. Field of the Invention
This invention relates to an ultrasonic apparatus and method based on resonance frequencies for determining unknown parameters in a multilayer structure, such as thickness, elastic properties of individual layers, or bonding strength between layers. The method is of particular interest when the thickness of the multilayer structure is less than two millimeters or when the ultrasound is generated by a laser.
2. Description of Prior Art
Ultrasonic measurement techniques generally refers to the principle of generating an ultrasonic pulse in an object, and then detecting the signal after propagation in the object to determine its geometrical, microstructural, and physical properties. This technique is advantageous because it is nondestructive. Conventional ultrasonic devices have been developed which involves the use of transducers, including piezoelectric and electromagnetic acoustic transducers (EMATs). Another ultrasonic device is based on laser-ultrasonics, wherein one laser with a short pulse is used for generation and another one, long pulse or continuous, coupled to an optical interferometer is used for detection. Either laser may be coupled through an optical fiber for ease of handling. This approach is advantageous because it does not require either the generation laser or the laser-interferometer detector to be close to the object. Furthermore, unlike an EMAT or piezoelectric transducer, the generation laser and laser-interferometer are not subject to precise orientation requirements. Details about laser-ultrasonics can be found in C. B. Scruby, L. E. Drain, xe2x80x9cLaser-ultrasonics: techniques and applicationsxe2x80x9d, Adam Hilger, Bristol, UK 1990 and J. -P. Monchalin, xe2x80x9cOptical detection of ultrasound,xe2x80x9d IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 33,485 (1986).
To determine material properties from detected signal, usually the time of flight (TOF) method is used, which consists in measuring the time that the ultrasonic pulse takes to travel from the point of generation to the point of detection. This travel time relates to the travel distance and ultrasonic velocity which depends on some elastic properties, and knowing one parameter allows to get the other. For thickness measurement or properties in the thickness direction, the detection is made on the opposite side of the object aligned with the generation point, or on the same side and close to the generation point. This conventional method for determining properties of an object is limited to materials having a thickness which is relatively large compared to the wavelength of the ultrasonic pulse used. Otherwise, ultrasonic waves reflected from the front and back surfaces of a thin object ( less than 2 mm) overlap and interfere in the time domain, precluding any measurement of time-of-flight. The generation of an ultrasonic pulse with smaller wavelength or high frequency content for cases of thin specimen may be limited by availability and costs associated with such an instrumentation.
The situation is even worst for multilayer structures comprising several layers of different materials with a finite bonding strength between layers. For multilayer structure with thick enough layers with respect to the ultrasonic wavelength, direct application of the TOF method is possible provided that a proper identification of reflected pulses is made with each layer. Recent examples are found in the U.S. Pat. No. 5,866,819 (Albu et al.) and U.S. Pat. No. 5,974,886 (Carroll et al.). For thinner multilayer structures, more refined techniques have been developed in recent years still analyzing the detected signal in the time domain. Examples of methods used are reduction of pulse duration with a deconvolution technique as found in the U.S. Pat. No. 5,723,791 (Koch et al.), comparison of detected waveform with a set of reference waveforms as in the U.S. Pat. No. 5,038,615 (Trulson et al.) and analyzing the interfering ultrasonic tone-bursts (narrowband signal, typically of about ten cycles in duration) with selected frequencies as in U.S. Pat. No. 5,608,165 (Mozurkewich).
The ultrasonic spectroscopy method is an alternative for this purpose. Closely related with the latter application, constructive or destructive interference between reflected tone-bursts at a particular frequency arising from propagation of an ultrasonic wave between the boundaries of the object corresponds to an ultrasonic resonance. For example, an ultrasonic resonance can arise in a plate when an ultrasonic wave propagates in the thickness direction and that the plate thickness corresponds to an integral multiple of half the wavelength of the ultrasonic wave. A longitudinal resonance refers to an ultrasonic resonance of a longitudinal wave, i.e., of an elastic wave polarized in the propagation direction. A shear resonance refers to an ultrasonic resonance of a shear wave, i.e., of an elastic wave polarized in a direction perpendicular to the propagation direction. In this method, a tone-burst is generated with a selected frequency, the signal detected is digitized and analyzed into the frequency domain typically by using the Fast Fourier Transform to get amplitude or phase information. By sweeping the frequency of the generated tone-burst and processing the each detected signal over the range of interest, the frequency response is obtained to identify resonances. Examples of applications using the frequency response but without relying on resonances are found in the U.S. Pat. No. 5,305,239 (Kinra), U.S. Pat. No. 5,663,502 (Nagashima et al.). Examples of those using the resonance information are found in U.S. Pat. Nos. 4,305,294 (Vasile et al.), 5,062,296 (Migliori), and more recently, U.S. Pat. No. 5,591,913 (Tucker). This method has the limitation of a long acquisition time as well as processing time, even with very recent improvements as in the U.S. Pat. No. 6,023,975 (Willis).
A different ultrasonic spectroscopy method is to launch a wideband pulse either with a transducer or with a radiation source like a laser and to analyze the single interaction signal comprising several reflected pulses or echoes into the frequency domain. The interference between overlapping echoes produces resonance dips or peaks in the amplitude of the frequency response. This method has been used with success, the overlapping of echoes can be very high, and the resonances are usually sharp enough to get a very good estimate of material properties, even with a moderately high level of attenuation. However, as in the previous method, this is mostly used for single plate or sheet of one material. A recent example from one of the inventors, measuring longitudinal as well as shear resonances with laser-ultrasonics to get material properties including texture in metal sheets, can be found in the U.S. Pat. No. 6,057,927 (Levesque et al.). For multilayer structure, an intricate coupling between resonance modes occurs which requires a more careful analysis to get any material properties. With the presence of a fluid between layers, the resonance modes are mainly those of individual layers in vacuum and an inversion algorithm has been successfully applied to recover some properties. For adhesively bonded layers, the resonance modes of the individual layers are strongly coupled and important frequency shifts are observed. The sensitivity of the ultrasonic signal to adhesive bond strength and the possibility of its determination is found in the U.S. Pat. No. 5,408,881 (Piche et Levesque), from one of the inventors. It is generally found that a model for propagation of ultrasound is essential to determine any unknown parameter from a multilayer structure.
It is an object of the present invention to alleviate the afore-mentioned disadvantages of the prior art.
According to the present invention there is provided a method for determining layer thickness or other parameters of a multilayer structure, comprising the steps of producing an ultrasonic pulse in the multilayer structure for interaction therewith over a range of frequencies to obtain a time-dependent interaction signal characteristic of the multilayer structure; detecting the interaction signal from the said multilayer structure; transforming said time-dependent interaction signal from the time domain to the frequency domain to obtain the frequency response of the said multilayer structure; determining locations of peak or dip values over the range of frequencies from said frequency response of the said multilayer structure to obtain a set of measured resonance frequencies; using a mathematical model describing the behaviour of said multilayer structure and containing at least one variable parameter to predict resonance frequencies for said multilayer structure; and adjusting said at least one variable parameter in said mathematical model to obtain a best fit of said predicted resonance frequencies with said measured resonance frequencies to thereby obtain said at least one variable parameter.
The mathematical model is preferably a characteristic equation derived from appropriate boundary conditions and given by:       "LeftBracketingBar"                                                      B              +                        ⁢            T                                                            B            -                                "RightBracketingBar"    =  0
where |xe2x80xa2| is the determinant of a matrix, T is the global matrix of the multilayer structure, and matrices B+ and B+ relates to the particular boundary conditions applied on the vectors combining displacements and tractions, of both the top and bottom surfaces.
The invention thus provides an apparatus and method using ultrasonic spectroscopy and a model that can be reduced in a characteristic equation, specifically oriented for predicting resonance frequencies, to determine the thickness, elastic properties and adhesion strength of a general multilayer structure. The method is of particular interest when the thickness of the multilayer structure is less than two millimeters or when the ultrasound is generated by a laser. The use of a characteristic equation is more efficient, and can result in a reduction factor of at least 10 in processing time.
The present invention also provides a system for determining layer thickness and other parameters of a multilayer structure, comprising an ultrasonic pulse generator for generating an ultrasonic pulse in the multilayer structure for interaction therewith over a range of frequencies to obtain a time-dependent interaction signal characteristic of the multilayer structure; a detector for detecting the interaction signal from the said multilayer structure; a spectrum analyzer for transforming said interaction signal into the frequency domain to obtain a measured frequency response; and a processor for calculating from a mathematical model of said multilayer structure predicted resonance frequencies and obtaining a best fit of said predicted resonance frequencies with said measured frequency response by adjusting at least one parameter in said mathematical model, thereby to obtain said at least one parameter.
Preferably, the said spectrum analyzer determines the resonance frequencies and said processor matches the measured resonance frequencies with predicted resonance frequencies from said mathematical model to obtain said at least one parameter.